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Question : If $a =\cot A+\cos A$ and $b =\cot A-\cos A$, then find the value of $a^2-b^2-4 \sqrt{ab}$.
Option 1: 0
Option 2: –1
Option 3: 1
Option 4: –4
Correct Answer: 0
Solution : $a =\cot A+\cos A$ $b =\cot A-\cos A$ We have to find the value of $a^2-b^2-4 \sqrt{ab}$. $= (\cot A+\cos A)^{2}-(\cot A-\cos A)^{2}-4\sqrt{(\cot A+\cos A)(\cot A-\cos A)}$ $= \cot^{2} A+\cos^{2} A+2\cot A\times \cos A-(\cot^{2} A+\cos^{2} A-2\cot A\times \cos A)-4\sqrt{\cot^{2}A-\cos^{2}A}$ $= (\cot^{2} A+\cos^{2} A+2\cot A\times \cos
Question : If $\frac{3x-1}{x}+\frac{5y-1}{y}+\frac{7z-1}{z}=0$, what is the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}?$
Option 1: –3
Option 2: 0
Option 3: 15
Option 4: 21
Correct Answer: 15
Solution : Given: $\frac{3x-1}{x}+\frac{5y-1}{y}+\frac{7z-1}{z}=0$ ⇒$3-\frac{1}{x}+5-\frac{1}{y}+7-\frac{1}{z}=0$ ⇒$\frac{1}{x} + \frac{1}{y}+\frac{1}{z}= 3+5+7=15$ Hence, the correct answer is 15.
Question : A circle is circumscribing a triangle whose sides are 30 cm, 40 cm, and 50 cm. Find the circumference of the circle.
Option 1: $75 \pi$ cm
Option 2: $25 \pi$ cm
Option 3: $100 \pi$ cm
Option 4: $50 \pi$ cm
Correct Answer: $50 \pi$ cm
Solution : Given, the sides of the triangle are 30 cm, 40 cm, and 50 cm. 30 cm, 40 cm, and 50 cm form a pythagorean triplet. In a right triangle, the circumradius (radius of the circle circumscribing the triangle) is half the length of
Question : Shinzo Abe, who recently died, served as the Prime Minister of:
Option 1: North Korea
Option 2: Japan
Option 3: South Korea
Option 4: Thailand
Correct Answer: Japan
Solution : The correct option is Japan.
Shinzo Abe served as Prime Minister of Japan. He held the office in two separate terms: firstly, from 2006 to 2007 and then again from 2012 to 2020. He was the longest-serving Prime Minister of Japan, making him a
Question : Directions: Select the correct option that indicates the arrangement of the following terms in a logical and meaningful order. 1. Answer writing 2. Answer book 3. Admit card 4. Question paper 5. Examination form
Option 1: 3–5–2–4–1
Option 2: 5–3–2–4–1
Option 3: 3–2–4–1–5
Option 4: 5–2–3–1–4
Correct Answer: 5–3–2–4–1
Solution : Given: 1. Answer writing 2. Answer book 3. Admit card 4. Question paper 5. Examination form
The stages for writing an exam are as follows – First, a student has to fill out the examination form, then after successfully submitting of exam form a student
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
They have not and cannot be in the good books of the coach because they lack discipline.
(1) have not and can never been
(2) have not been and can never be
(3) have not and can never be
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The correct choice will be the second option.
The second option, "they have not been and can never be in the good books of the coach because they lack discipline" provides this parallel structure by placing both verbs in the same form, using have not
Question : Pipe A can fill an empty tank in 30 hours and B can fill it in 10 hours. Due to a leakage in the tank, it takes pipes A and B together 1.5 hours more to fill completely than it would have otherwise taken. What is the time taken by the leakage alone to empty the same tank completely, starting when the tank is completely full?
Option 1: 42 hours
Option 2: 40 hours
Option 3: 36 hours
Option 4: 45 hours
Correct Answer: 45 hours
Solution : Time taken by pipe A to fill a tank = 30 hours Part of tank filled by pipe A in an hour = $\frac{1}{30}$ Time taken by pipe B to fill a tank = 10 hours Part of tank filled by pipe B in
Question : The Working Committee of the National Congress sanctioned the resolution named 'Quit India' at
Option 1: Wardha
Option 2: Nagpur
Option 3: Mumbai
Option 4: Delhi
Correct Answer: Wardha
Solution : The correct answer is Wardha.
In July 1942, the Congress Working Committee convened in Wardha, where they adopted a comprehensive resolution calling for the immediate cessation of British rule in India. This resolution is commonly referred to as the "Quit India Resolution."
Question : Directions: If + means ÷, – means +, × means – and ÷ means ×, then what will come in place of (?) in the given equation? 5 ÷ 2 – 20 + 5 × 2 = ?
Option 1: 12
Option 2: 15
Option 3: 20
Option 4: 10
Correct Answer: 12
Solution : Given + means ÷, – means +, × means – and ÷ means × 5 ÷ 2 – 20 + 5 × 2 = ?
After interchanging the symbols the equation becomes – = 5 × 2 + 20 ÷ 5 – 2 = 10
Question : Refer to the following data table and answer the question.
Between 10 pm to 6 am, a fitness band records the following data. How long was the user in Light sleep or Extremely light sleep?
Option 1: 4.4 hours
Option 2: 3.9 hours
Option 3: 2.9 hours
Option 4: 4.9 hours
Correct Answer: 4.4 hours
Solution : According to the data given, Total time = 10 PM to 6 AM = 8 hours The user in light Sleep or extremely light sleep = 30% + 25% = 55% So, the time spend by user = $\frac{55}{100}\times8$ = 4.4 Hence, the correct
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